to enroll in courses, follow best educators, interact with the community and track your progress.
14 lessons,
2h 33m
Enroll
815
Bernoulli's Equation (Linear Differential Equation Form)
370 plays

More
This lesson discusses the concept of Bernoulli's equation to make the differentiable reducible to linear differential equation form. This is for jee main and advanced

## Vineet Loomba is teaching live on Unacademy Plus

Vineet Loomba
IITian | No. 1 Educator in IIT-JEE | 6 Million Minutes Watch Time | 8+ Years Experience | Youtube: Maths Wallah | vineetloomba.com

U
sir how to decide whether to tske dr/d0 or do/dr?
sir pls solve first two questions
Vineet Loomba
7 months ago
Thanks ..dont forget to rate 5 stars
Abhishek Sharma
6 months ago
extraordinary
Abhishek Sharma
6 months ago
sit
1. DIFFERENTIAL EqUATIONS (DETAILED COURSE) JEE MAIN AND ADVANCED IIT-IEE MATHS MADE EASY PREPARED BY: ER. VINEET LOOMBA IITiAN | IIT-JEE MENTOR FoR SURE SHoT SUcCESS IN JEE MAIN AND ADVANCED (IIT-JEE)

2. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) ABOUT ME B.Tech. From IIT Roorkee -\$ IIT-JEE Mentor Since 2010. -^ Doubts/Feedback in Comment Section * Comment other topics you want to revise. * Follow me @ https://unacademy.com/user/vineetloomba to get unacademy updates or search me on Google * Share among your peers as SHARING is CARING!!

3. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Other Detailed Courses Made so far on Unacademv: V Strategy for JEE Main and Advanced V Sets, Relations and Functions V Trigonometry V Applications of Derivatives Limits, Continuity. Differentiability V Indefinite Integration V Definite Integration Complex Number V Logarithmic Functions V Sequences Series V Most Important Questions in IIT-JEE Permutations Combinations Binomial Theorem V Straight Lines V Applications of Integrals V Circles (Detailed Course) V Probability MathematicS V Parabola (Detailed Course) v Inverse Trigonometry V Mathematical Reasoning V Ellipse (Detailed Course) V Hyperbola V Differential Equations Upcoming Courses next month: Statistics Matrices Determinants MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

4. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example: Solution: Solve sec2 d + tan (1-r tan )dr-0 ,. The given equation can be written as dr. Sec2 sec2 ie.tan'e dr tane l.e cosec2 d .cou dr Using the transformation MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

5. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (11T-JEE) Using the transformation cot -u, we get-cosec, d du the equation reduces to du dr whose IF. Hence, the solution of the given differential equation is given by i.e. u=r-1+Cer ie, cot -r-1 + Cer. MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

6. FOR 100% SUCCESS N JEE MAIN AND ADVANCED (IIT-JEE) Bernoulli's equation dy Equations of the form dx + Py Q.yn, n 0 and n # 1 where P and Q are functions of x, is called Bernoulli's equation Divide by y 2. Put y-n+1 v. MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

7. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (11T-JEE) 2 , dy-y-y (Bernoulli's equation) Example Solve dx Solution. Dividing both sides by y2 1 dy 1 1 y2 dk xy x .(1) 1 dy dt Putting y = t : differential equation (1) becomes, dt 1 dt t 1 dt +--which is linear differential equation in dx X x MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

8. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) dx General solution is x dx C -Inx C ER. VINEET LOOMBA (IIT RooRKEE) MATHEMATICS FOR IIT-JEE

9. FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) SELF PRACTICE PROBLEMS 2 Solve x (x2 + 1) y (1 - X2) + x2 Inx dx Ans: y2 (x2 + 1 + ce Ans: X y (c + y2) Ans: x1ny = e"(x-1) + c 3 Solve: ( +2y') X y dx dx MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

10. 100% SUCCESS IN JEE MAIN AND ADVANCED Save . Save for this Course (Free) MOST IMPORTANT QUESTIONS IN MATHEMATICS JEE MAIN AND ADVANCED . Recommend Lessons (Like) PREPARED BY ER. VINEST LOOMSA ITIAN | IT-IEE MENTOR IT-FEE MATHS MADE CASY Rate and Review the Course . Comments . Sharing with friends 00:00 05:46 SURE SROT Success IEE MAlm AND ADVANCED CtIT-IEE) 91 likes 18 comments A Share HINDI Crash Course Maths (Hindi) Most Important Questions in IIT-JEE Mathematics (Chapter- Wise) Vineet Loomba Follow 11k Followers 5.0 (51 ratings) Edit review